[5] In 2007 Trapani won the Gaudeamus Award for young contemporary composers[6] for his composition Sparrow Episodes, for ensemble with solo electric guitar, which was performed in the Muziekgebouw aan 't IJ in Amsterdam by the Asko Ensemble under Étienne Siebens, with Trapani on guitar.
[8] His composition Rust and Stardust was performed during the Tectonics Festival in Glasgow in 2015; the Guardian reviewer found it "accomplished and dreary",[9] while The Scotsman spoke of "kaleidoscopic explosions that ... gave structure and shape to its insistently concise material".
[10] Also in 2015, Trapani was among the recipients of a Charles Ives Scholarship for promising students from the American Academy of Arts and Letters,[11] and received a commission from Chamber Music America.
[13] In 2018 the Koussevitzky Foundation of the Library of Congress commissioned him to write a work for the Spektral Quartet.
[14] In 2019 he received both a Guggenheim Fellowship[15] and a commission from the Fromm Music Foundation of Harvard University.